Linear-time algorithms for problems on planar graphs with fixed disk dimension
The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties of graphs with a given disk dimension are derived, leading to an algorithm to obtain an outerplanar subgraph of a graph w...
محفوظ في:
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| التنسيق: | article |
| منشور في: |
2007
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/2777 http://dx.doi.org/10.1016/j.ipl.2006.08.006 http://www.sciencedirect.com/science/article/pii/S0020019006002511 |
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| الملخص: | The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties of graphs with a given disk dimension are derived, leading to an algorithm to obtain an outerplanar subgraph of a graph with disk dimension k by removing at most 2k−2 vertices. This reduction is used to obtain linear-time exact and approximation algorithms on graphs with fixed disk dimension. In particular, a linear-time approximation algorithm is presented for the pathwidth problem. |
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